Question

1) The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x-3 and g(x) = 3x+8. Find f(x) multiplied by g(x). 2) The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = x^2+x-20 and g(x)=x+5. Find f(x)/g(x) <-- (this is a fraction.) 3) Evaluate the piecewise function at x=-3 and x-11. 4) Find the inverse of the function. F(x) = 3x+7.

Answer 1

1)6x^2+7x-24

2) x-4

3) f(-3)=-14 g(-3)=2 f(-3)/g(-3)=-7 and p(-3)=-3-4=-7

f(-11)=90 g(-11)=-6 f(-11)/g(-11)=-15 and p(-11)=-11-4=-15

4)f'(x)=(x-7)/3

Explanation:

1) f(x)=2x-3 g(x)=3x+8

f(x)*g(x)=m(x)=(2x-3)(3x+8)=6x^2+16x-9x-24=6x^2+7x-24

2) f(x)=x^2+x-20 g(x)=x+5

f(x)/g(x)=p(x)=(x^2+x-20)/(x+5)=> by finding the roots of f(x) we obtain =

(x-4)(x+5)/(x+5)--->f(x)/g(x)=p(x)=(x-4)

3) f(-3)=-14 g(-3)=2 f(-3)/g(-3)=-7 and p(-3)=-3-4=-7

f(-11)=90 g(-11)=-6 f(-11)/g(-11)=-15 and p(-11)=-11-4=-15

4) If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back x

y=3x+7

(y-7)/3=x=--> f'(x)=(x-7)/3